# Indicative Conditionals

## Abstract

“Either the butler or the gardener did it. Therefore, if the butler didn’t do it, the gardener did.” This piece of reasoning — call it the *direct argument* — may seem tedious, but it is surely compelling. Yet if it is a valid inference, then the indicative conditional conclusion must be logically equivalent to the truth-functional material conditional,^{1} and *this* conclusion has consequences that are notoriously paradoxical. The problem is that if one accepts the validity of the intuitively reasonable direct argument from the material conditional to the ordinary indicative conditional, then one must accept as well the validity of many arguments that are intuitively absurd. Consider, for example, “the butler did it; therefore, if he didn’t, the gardener did.” The premiss of this argument entails the premiss of the direct argument, and their conclusions are the same. Therefore, if the direct argument is valid, so is this one. But this argument has no trace of intuitive plausibility. Or consider what may be inferred from the *denial* of a conditional. Surely I may deny that if the butler didn’t do it, the gardener did without affirming the butler’s guilt. Yet if the conditional is material, its negation entails the truth of its antecedent. It is easy to multiply paradoxes of the material conditional in this way — paradoxes that must be explained away by anyone who wants to defend the thesis that the direct argument is valid.

## Keywords

Selection Function Conditional Statement Direct Argument Indicative Conditional Pragmatic Theory## Preview

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## Notes

- 3.Photo-copies have been widely circulated; part of it has been recently published in: D. Davidson and G. Harman (eds.),
*The Logic of Grammar*, Dickenson, Encino, Cal., 1975, pp. 64–75.Google Scholar - 4.See David Lewis,
*Counterfactuals*, Harvard University Press, Cambridge, 1973, pp. 84–91 for a defense of realism about possible worlds.Google Scholar - 5.See M. J. Cresswell,
*Logics and Languages*, Methuen, London, 1973, pp. 23–24,Google Scholar - 5a.and Stalnaker, ‘Pragmatics,’ in G. Harman and D. Davidson (eds.),
*Semantics of Natural Languages*, Reidel, Dordrecht, 1972, pp. 381–82 for brief discussions of the intuitive motivation of this definition of proposition.Google Scholar - 6.For a fuller discussion and defense of this concept, see Stalnaker, ‘Presuppositions’,
*Journal of Philosophical Logic*, (1973), 447–457.Google Scholar - 8.Stalnaker, ‘A Theory of Conditionals’, in N. Rescher (ed.),
*Studies in Logical Theory*, Blackwell, Oxford, 1968, pp. 98–112,Google Scholar - 8a.and Stalnaker and R. H. Thomason, ‘A Semantic Analysis of Conditional Logic’,
*Theoria*,**36**(1970), 23–42. See also Lewis,*Counterfactuals*. The formal differences between Lewis’s theory and mine are irrelevant to the present issue.CrossRefGoogle Scholar - 12.
- 15.